The number 84240
84240 is a composite number with 100 divisors. Its prime factorisation is × × 5 × 13. Divisors (100): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 24 … 84240.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 84240: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
84240 is composite. Its prime factorisation is
- 3
The divisors add up to 315084; without 84240 itself that is 230844, so 84240 is abundant (230844 is more than 84240). Euler's totient φ(84240) = 20736 numbers up to 84240 share no factor with it.
- 4
The digits of 84240 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 84240 = 2^{4} \times 3^{4} \times 5 \times 13 \]84240 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 100 |
| Sum of divisors | 315084 |
| Euler totient φ(n) | 20736 |
| Square | 7096377600 |
| Cube | 597798849024000 |
| Square root | 290.241279 (= 36√65) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 45 |
| Scientific notation | 8.424 × |
84240 in other forms
| Form | Value |
|---|---|
| In words | eighty-four thousand two hundred and forty |
| Binary (base 2) | 10100100100010000 |
| Octal (base 8) | 244420 |
| Hexadecimal (base 16) | 14910 |
| Base 3 | 11021120000 |
| As time | 84240 seconds = 23 h 24 min 0 s |
Is 84240 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (84240 ÷ 2 = 42120) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (84240 ÷ 3 = 28080) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (84240 ÷ 4 = 21060) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (84240 ÷ 5 = 16848) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (84240 ÷ 6 = 14040) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (84240 ÷ 8 = 10530) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (84240 ÷ 9 = 9360) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (84240 ÷ 10 = 8424) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (84240 ÷ 12 = 7020) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 84240 a prime number?
No. 84240 = × × 5 × 13, so it is divisible by 2.
What are the factors of 84240?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 24, 26, 27, 30, 36, 39, 40, 45, 48, 52, 54, 60, 65, 72, 78, 80, 81, 90, 104, 108, 117, 120, 130, 135, 144, 156, 162, 180, 195, 208, 216, 234, 240, 260, 270, 312, 324, 351, 360, 390, 405, 432, 468, 520, 540, 585, 624, 648, 702, 720, 780, 810, 936, 1040, 1053, 1080, 1170, 1296, 1404, 1560, 1620, 1755, 1872, 2106, 2160, 2340, 2808, 3120, 3240, 3510, 4212, 4680, 5265, 5616, 6480, 7020, 8424, 9360, 10530, 14040, 16848, 21060, 28080, 42120, 84240.
What is 84240 in binary?
10100100100010000 (hexadecimal 14910, octal 244420).
What is the square root of 84240?
About 290.2413, exactly 36√65.
Is 84240 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 84240?
84240 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.